Agile satellite earth observation time window calculation method

Abstract

The invention discloses an agile satellite earth observation time window calculation method, and belongs to the technical field of satellite earth observation. The invention aims to solve the problem that the existing method for calculating the earth observation time window of the agile satellite through orbit recursion is difficult to realize on-orbit long-time task planning due to large calculation amount. Comprising the steps of performing orbit recursion by considering J2 perturbation according to six orbit elements and flight time of an earth observation satellite, converting a position vector into geographic longitude and latitude by considering the influence of earth rotation, and establishing an analytical expression of a sub-satellite point trajectory about time; according to the sub-satellite point trajectory expression of the satellite, screening out moments equal to the latitude of the ground target, and judging whether the moments meet relative distance constraints or not, so as to estimate moments with observation conditions; an observation attitude angle is calculated according to a relative position vector of a satellite pointing target, constraints of a maximum roll angle and a pitch angle are considered, and an over-top moment and an observation time window are iteratively solved near an estimation moment. The method is used for calculating the earth observation time window of the satellite.

Description

Technical Field

[0001] The invention relates to a method for calculating a time window for an agile satellite to observe the earth, and belongs to the technical field of satellite earth observation. Background Art

[0002] As the number of Earth observation satellites in orbit gradually increases, how to achieve autonomous satellite mission planning has become a key problem that needs to be solved urgently to reduce the cost of manual control on the ground. In order to meet user needs, Earth observation satellites need to complete the observation tasks of multiple ground targets within a specified time. Due to the limited performance of onboard computers, satellites in orbit need an efficient and simple method to calculate the observation time window for ground targets and plan their missions accordingly.

[0003] Earth observation satellites are equipped with high-resolution payloads, which can be used to observe ground targets by adjusting their attitude when flying over them. Agile satellites can quickly perform three-axis maneuvers compared to traditional non-agile satellites, which greatly increases the observation time window for targets and allows them to plan their own observation mission time. The traditional method for calculating the time window for Earth observation is to complete orbit recursion within a specified time in advance and traverse all time nodes to see if they meet the observation constraints. This method is difficult to achieve long-term mission planning in orbit due to its large amount of calculation. Summary of the invention

[0004] In view of the problem that the existing method of calculating the time window for agile satellite to observe the earth through orbit recursion is difficult to implement long-term mission planning on orbit due to the large amount of calculation, the present invention provides a method for calculating the time window for agile satellite to observe the earth.

[0005] A method for calculating a time window for an agile satellite to observe the earth of the present invention comprises:

[0006] According to the initial values ​​of the six orbital elements of the earth observation satellite and the initial flight time, orbit recursion is performed considering the J2 perturbation to obtain the six orbital elements of the satellite at time t; based on the six orbital elements of the satellite at time t, the position vector of the earth observation satellite in the geocentric inertial coordinate system and the velocity vector in the geocentric inertial coordinate system at time t are calculated;

[0007] The position vector of the earth observation satellite in the geocentric fixed coordinate system is calculated from the position vector in the geocentric inertial coordinate system; the position vector in the geocentric fixed coordinate system is converted into a sub-satellite point represented by geographic longitude and geographic latitude, and an analytical expression of the sub-satellite point trajectory with respect to time is obtained;

[0008] Based on the analytical expression of the sub-satellite point trajectory with respect to time, all moments when the sub-satellite point and the ground target have the same latitude are selected; then, based on all the selected moments, the corresponding haversine distances between the sub-satellite point and the ground target are calculated; the moment when the haversine distance is less than the set distance threshold is taken as the estimated moment when the visible time window exists;

[0009] The three-axis unit vector of the earth observation satellite in the orbital coordinate system is calculated from the position vector of the earth observation satellite in the geocentric inertial coordinate system and the velocity vector in the geocentric inertial coordinate system at the estimated time, and then the projection of the relative position vector of the sub-satellite point and the ground target in the orbital coordinate system at the estimated time is calculated; the expressions of the target roll angle and the target pitch angle at the estimated time are obtained by combining the attitude angle of the earth observation satellite; the target pitch angle expression is iterated by a numerical method to obtain the overpass time, and then the target roll angle is determined based on the overpass time; the overpass time corresponding to the target roll angle satisfying the maximum roll angle constraint is used as the selected overpass time with an observation time window;

[0010] The observation time window corresponding to the selected overpass time is obtained by iterative calculation based on the start and end time constraints of the observation time window, and is used as the final agile satellite earth observation time window.

[0011] According to the method for calculating the time window of agile satellite earth observation of the present invention, the method for calculating the six satellite orbit numbers at time t is:

[0012] The six elements of the satellite orbit are expressed as [aei Ω ω M], where a is the semi-major axis of the orbit, e is the eccentricity, i is the inclination, Ω is the right ascension of the ascending node, ω is the angular distance of the periapsis, and M is the mean anomaly;

[0013] In the orbit recursion, the influence of the non-spherical gravity J2 perturbation term is considered, and the time t0 is taken as the initial time of the flight. The six satellite orbit elements at time t are calculated based on the linearized J2 perturbation equation:

[0014]

[0015] Where a0 is the initial value of the semi-major axis of the orbit at time t0, e0 is the initial value of the eccentricity at time t0, i0 is the initial value of the inclination at time t0, Ω0 is the initial value of the right ascension of the ascending node at time t0, ω0 is the initial value of the angular distance of the pericenter at time t0, and M0 is the initial value of the mean anomaly at time t0; J2 is the perturbation coefficient, n is the average orbital angular velocity, μ is the Earth's gravitational constant; is the earth's equatorial radius, p is the semi-diameter, p = a0(1-e 2 ).

[0016] According to the method for calculating the time window of the agile satellite earth observation of the present invention, the position vector of the earth observation satellite at time t in the geocentric inertial coordinate system is expressed as r ECI :

[0017]

[0018] Where f is the true anomaly angle;

[0019] The velocity vector in the geocentric inertial coordinate system is represented by v ECI :

[0020]

[0021] According to the method for calculating the time window for earth observation by an agile satellite of the present invention, the position vector of the earth observation satellite in the geocentric fixed coordinate system is expressed as r ECEF :

[0022] r ECEF =R Z (α Gt )r ECI ,

[0023] Where R Z is the rotation matrix of the earth observation satellite around the Z axis in the geocentric inertial coordinate system, α Gt is Greenwich Mean Sidereal Time, α G0 is the initial Greenwich mean sidereal time, is the angular velocity of the Earth's rotation.

[0024] According to the method for calculating the time window of the agile satellite earth observation of the present invention, the method for obtaining the analytical expression of the sub-satellite point trajectory with respect to time is:

[0025] According to r ECEF =[r x ,r y ,r z ] T Calculate the geocentric longitude λ c and geocentric latitude

[0026] λ c =arctan2(r y ,r x ),

[0027] Where r x is the X-axis coordinate of the geocentric fixed coordinate system, r y is the Y-axis coordinate of the geocentric fixed coordinate system, r z is the Z-axis coordinate of the geocentric fixed coordinate system;

[0028] Geographic longitude λ d for:

[0029]

[0030] Where u is the latitude angle: u = ω + f;

[0031] According to the latitude argument u, the geocentric latitude It is expressed as:

[0032]

[0033] Geographic latitude for:

[0034]

[0035] In the formula is the first eccentricity of the Earth ellipsoid;

[0036] By the geographical longitude λ at all times d and geographic latitude The sub-satellite point represented by is used to obtain the analytical expression of the sub-satellite point trajectory with respect to time.

[0037] According to the agile satellite earth observation time window calculation method of the present invention, the method of screening out all the moments when the sub-satellite point is equal to the latitude of the ground target is:

[0038] When the latitude of the sub-satellite point is equal to that of the ground target, the latitude argument u satisfies:

[0039]

[0040] Where N is the number of satellite orbits;

[0041] For a near-circular orbit: f≈M; then the latitude argument u is linearly related to t, and all moments when the sub-satellite point and the ground target latitude are equal can be calculated by the linearized J2 perturbation equation.

[0042] According to the agile satellite earth observation time window calculation method of the present invention, the method for determining the estimated time when there is a visible time window is:

[0043] Calculate the haversine distance d:

[0044]

[0045] In the formula is the current geographic latitude difference between the sub-satellite point and the ground target, is the current geographic latitude of the subsatellite point, is the current geographic latitude of the ground target; Δλ is the current geographic longitude difference between the sub-satellite point and the ground target;

[0046] If the haversine distance d is less than the set distance threshold, the current time is used as the estimated time.

[0047] Beneficial effects of the present invention: The method of the present invention uses an analytical approximate model to replace orbital integration, and uses constraint screening to replace traversal judgment. The amount of calculation is extremely small, and it can be applied to the calculation of the time window for long-term earth observation by satellites in orbit, providing sufficient preparation for autonomous mission planning. The method of the present invention is based on the linearized J2 perturbation model and takes into account the influence of the earth's rotation, and describes the sub-satellite point trajectory as an analytical expression related to time. The time that meets the observation conditions is screened out according to the longitude and latitude difference and the relative distance, and the observation time window is obtained by iterative calculation near it. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flow chart of the method for calculating the time window for earth observation by an agile satellite according to the present invention;

[0049] Figure 2 It is a schematic diagram of the observation time window;

[0050] Figure 3 It is a simulation diagram of the observation time window in a specific embodiment. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0053] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0054] Specific implementation method 1. Combination Figure 1 and Figure 2 As shown, the present invention provides a method for calculating a time window for an agile satellite to observe the earth, comprising:

[0055] According to the initial values ​​of the six orbital elements of the earth observation satellite and the initial flight time, orbit recursion is performed considering the J2 perturbation to obtain the six orbital elements of the satellite at time t; based on the six orbital elements of the satellite at time t, the position vector of the earth observation satellite in the geocentric inertial coordinate system and the velocity vector in the geocentric inertial coordinate system at time t are calculated;

[0056] The position vector of the earth observation satellite in the geocentric fixed coordinate system is calculated from the position vector in the geocentric inertial coordinate system; the position vector is converted into geographic longitude and latitude considering the influence of the earth's rotation, that is, the position vector in the geocentric fixed coordinate system is converted into a sub-satellite point represented by geographic longitude and latitude, and an analytical expression of the sub-satellite point trajectory with respect to time is obtained;

[0057] Based on the analytical expression of the sub-satellite point trajectory with respect to time, all moments when the sub-satellite point and the ground target have the same latitude are selected; then, based on all the selected moments, the corresponding haversine distances between the sub-satellite point and the ground target are calculated; the moment corresponding to the time when the haversine distance is less than the set distance threshold is taken as the estimated moment when the visible time window exists; the estimated moment is the moment when the observation conditions are met;

[0058] The three-axis unit vector of the earth observation satellite in the orbital coordinate system is calculated from the position vector of the earth observation satellite in the geocentric inertial coordinate system and the velocity vector in the geocentric inertial coordinate system at the estimated time, and then the projection of the relative position vector of the sub-satellite point and the ground target in the orbital coordinate system at the estimated time is calculated; the expressions of the target roll angle and the target pitch angle at the estimated time are obtained by combining the attitude angle of the earth observation satellite; the target pitch angle expression is iterated by a numerical method to obtain the overpass time, and then the target roll angle is determined based on the overpass time; the overpass time corresponding to the target roll angle satisfying the maximum roll angle constraint is used as the selected overpass time with an observation time window;

[0059] The observation time window corresponding to the selected overpass time is obtained by iterative calculation based on the start and end time constraints of the observation time window, and is used as the final agile satellite earth observation time window.

[0060] Furthermore, the calculation method of the six satellite orbit numbers at time t is:

[0061] The six satellite orbit numbers are expressed as [aei Ω ω M] to describe the orbit state, where a is the semi-major axis of the orbit, e is the eccentricity, i is the inclination, Ω is the right ascension of the ascending node, ω is the angular distance of the periapsis, and M is the mean anomaly.

[0062] In the orbit recursion, the influence of the non-spherical gravity J2 perturbation term is considered, and the time t0 is taken as the initial time of the flight. Based on the linearized J2 perturbation equation (Gaussian perturbation equation), the six satellite orbit elements at time t are calculated:

[0063]

[0064] Where a0 is the initial value of the semi-major axis of the orbit at time t0, e0 is the initial value of the eccentricity at time t0, i0 is the initial value of the inclination at time t0, Ω0 is the initial value of the right ascension of the ascending node at time t0, ω0 is the initial value of the angular distance of the pericenter at time t0, and M0 is the initial value of the mean anomaly at time t0; J2 is the perturbation coefficient, J2=1.082627×10-3 , n is the average orbital angular velocity, μ is the Earth’s gravitational constant, μ=3.986×10 14 m 3 / s -2 ; is the Earth's equatorial radius, p is the semi-diameter, p=a0(1-e 2 ).

[0065] In this implementation, the position vector of the Earth observation satellite at time t in the geocentric inertial coordinate system (ECI) is expressed as r ECI :

[0066]

[0067] Where f is the true anomaly, which is equivalent to the mean anomaly;

[0068] The velocity vector in the geocentric inertial coordinate system is represented by v ECI :

[0069]

[0070] If only the effect of the earth's rotation is considered, the position vector of the satellite in the earth-centered fixed coordinate system (ECEF) can be calculated from the ECI position vector. The position vector of the earth observation satellite in the earth-centered fixed coordinate system is expressed as r ECEF :

[0071] r ECEF =R Z (α Gt )r ECI ,

[0072] Where R Z is the rotation matrix of the earth observation satellite around the Z axis in the geocentric inertial coordinate system, α Gt is Greenwich Mean Sidereal Time (GMST), α G0 is the initial Greenwich mean sidereal time, which can be calculated from the Coordinated Universal Time (UTC); is the angular velocity of the Earth's rotation.

[0073] Furthermore, the analytical expression of the subsatellite point trajectory with respect to time is obtained as follows:

[0074] According to r ECEF =[r x ,r y ,r z ] T Calculate the geocentric longitude λ c and geocentric latitude

[0075] λ c =arctan2(r y ,r x ),

[0076] Where r x is the X-axis coordinate of the geocentric fixed coordinate system, r y is the Y-axis coordinate of the geocentric fixed coordinate system, r z is the Z-axis coordinate of the geocentric fixed coordinate system;

[0077] Geographic longitude λ d The six orbital numbers can be expressed as:

[0078]

[0079] Where u is the latitude angle: u = ω + f;

[0080] According to the latitude argument u, the geocentric latitude It is expressed as:

[0081]

[0082] Geographic latitude for:

[0083]

[0084] In the formula is the first eccentricity of the Earth ellipsoid,

[0085] In summary, the satellite's geographic longitude and latitude at any time, that is, the sub-satellite point trajectory, can be obtained from the orbital state and flight time at the initial time. d and geographic latitude The sub-satellite point represented by is used to obtain the analytical expression of the sub-satellite point trajectory with respect to time.

[0086] Going further, the method to filter out all the moments when the latitude of the sub-satellite point is equal to that of the ground target is:

[0087] First, select a time in the satellite sub-satellite point trajectory that is close to the ground target latitude. When the sub-satellite point and the ground target latitude are equal, the latitude argument u satisfies:

[0088]

[0089] Where N is the number of satellite orbits;

[0090] For a near-circular orbit: f≈M; then the latitude argument u is linearly related to t, and all moments when the sub-satellite point and the ground target latitude are equal can be calculated by the linearized J2 perturbation equation.

[0091] The method for determining the estimated time when there is a visible time window is:

[0092] Determine whether the distance between the sub-satellite point and the ground target is less than the set threshold at the estimated time. Calculate the haversine distance d using the spherical triangle formula:

[0093]

[0094] In the formula is the current geographic latitude difference between the sub-satellite point and the ground target, is the current geographic latitude of the subsatellite point, is the current geographic latitude of the ground target; Δλ is the current geographic longitude difference between the sub-satellite point and the ground target;

[0095] If the haversine distance d is less than the set distance threshold, the current time is taken as the estimated time, that is, it is considered that there is a visible time window near the current time.

[0096] In this implementation, the satellite attitude is defined in the orbital coordinate system (VVLH), and the three-axis unit vector is expressed as [i jk] T , which can be obtained from the position and velocity vectors of the ECI system; where i is the X-axis unit vector of the orbital coordinate system, j is the Y-axis unit vector of the orbital coordinate system, and k is the Z-axis unit vector of the orbital coordinate system:

[0097] i=j×k,

[0098] The relative position vector δr of the earth observation satellite pointing to the ground target in the geocentric inertial coordinate system ECI for:

[0099] δr ECI =r T-ECI -r ECI ,

[0100] Where r T-ECI is the position vector of the ground target in the geocentric inertial coordinate system;

[0101] The projection of the relative position vector between the subsatellite point and the ground target in the orbital coordinate system at the estimated time is δr VVLH :

[0102] δr VVLH =[ijk] T ·δr ECI .

[0103] The position vector of the ground target in the geocentric inertial coordinate system needs to be converted from geographic longitude and latitude to the ECI system via the ECEF system. In order to accurately calculate the observation time window later, this conversion process needs to fully consider the effects of orbital perturbation, precession, nutation, polar motion, etc., rather than using the above analytical model.

[0104] Going further, the method for determining the time of passing the top is:

[0105] The attitude angle of the Earth observation satellite includes the roll angle φ, the pitch angle θ and the yaw angle ψ. Assume ψ = 0. The attitude rotation matrix R in the orbital coordinate system is yx =R y (θ)R x (φ), R x is the rotation matrix of the earth observation satellite around the X axis in the orbital coordinate system, R y is the rotation matrix of the earth observation satellite around the Y axis in the orbital coordinate system;

[0106] Assuming that the initial attitude of the Earth observation satellite payload points to the Z axis of the orbital coordinate system, then:

[0107]

[0108] The expressions of target roll angle and target pitch angle at the estimated time are obtained:

[0109]

[0110] Where δr x is the estimated time projection δr VVLH X-axis coordinate, δr y is the estimated time projection δr VVLH Y-axis coordinate, δr z is the estimated time projection δr VVLH The Z-axis coordinate of

[0111] The over-the-top moment is defined as the moment when the pitch angle θ = 0. At this time, the ground target can be observed only by rolling maneuvers. In the estimated time neighborhood, the expression of the pitch angle θ is iterated by a numerical method to obtain the over-the-top moment t over ; Set the top time t over Substituting the target roll angle expression into the target roll angle expression, the target roll angle is calculated; the numerical method may be the secant method;

[0112] If the target roll angle satisfies the maximum roll angle constraint, the current over-the-top time t over The selected passing moment as the existence observation time window.

[0113] The method for calculating the time window of agile satellite earth observation is:

[0114] Let the starting time of the observation time window be tstart and the end time t end Satisfy the maximum pitch angle constraint of the earth observation satellite:

[0115] θ(t start )=θ max ,θ(t end )=-θ max ,

[0116] θ max is the maximum elevation angle of the Earth observation satellite;

[0117] Set the starting time t start and the end time t end and the time t over The time interval is Δt:

[0118]

[0119] In t over ±Δt neighborhood, the final starting time t is determined iteratively using a numerical method for the pitch angle θ start and the final termination time t end , the final obtained [t start ,t end ] as the final agile satellite earth observation time window. The numerical method can be the secant method.

[0120] Example:

[0121] Assume that the initial orbital numbers of the agile earth observation satellite at UTC time 2024 / 7 / 1 4:00:00 are The maximum pitch and roll angles are both 45°, the geographical longitude and latitude of the ground target are (116.388°E, 39.9289°N), and the total mission duration is 3 days.

[0122] After analysis and calculation, there are 6 earth observation time windows in the total mission duration, and the start and end times and durations are shown in Table 1. The simulation results of the observation time windows are shown in Table 1. Figure 3 As shown, Figure 3 The trajectory of the mid-satellite point is represented by the blue dotted line, and the trajectory within the observation time window is represented by the green solid line, and both are distributed near the ground target represented by the star. Figure 3 It can be seen that this method can correctly calculate the earth observation time window.

[0123] Table 1 Calculation results of observation time window

[0124] Time window Start time (UTC) End time (UTC) Duration (seconds) 1 2024 / 7 / 1 8:41:22 2024 / 7 / 1 8:44:49 208 2 2024 / 7 / 2 2:06:21 2024 / 7 / 2 2:09:14 173 3 2024 / 7 / 2 8:51:41 2024 / 7 / 2 8:55:18 218 4 2024 / 7 / 3 2:16:48 2024 / 7 / 3 2:19:45 176 5 2024 / 7 / 3 7:21:22 2024 / 7 / 3 7:24:41 198 6 2024 / 7 / 4 0:46:20 2024 / 7 / 4 0:49:25 185

[0125] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A method for calculating the time window of an agile satellite earth observation, characterized in that: include: According to the initial values ​​of the six orbital elements of the earth observation satellite and the initial flight time, orbit recursion is performed considering the J2 perturbation to obtain the six orbital elements of the satellite at time t; based on the six orbital elements of the satellite at time t, the position vector of the earth observation satellite in the geocentric inertial coordinate system and the velocity vector in the geocentric inertial coordinate system at time t are calculated; The position vector of the earth observation satellite in the geocentric fixed coordinate system is calculated from the position vector in the geocentric inertial coordinate system; the position vector in the geocentric fixed coordinate system is converted into a sub-satellite point represented by geographic longitude and geographic latitude, and an analytical expression of the sub-satellite point trajectory with respect to time is obtained; Based on the analytical expression of the sub-satellite point trajectory with respect to time, all moments when the sub-satellite point and the ground target have the same latitude are selected; then, based on all the selected moments, the corresponding haversine distances between the sub-satellite point and the ground target are calculated; the moment when the haversine distance is less than the set distance threshold is taken as the estimated moment when the visible time window exists; The three-axis unit vector of the earth observation satellite in the orbital coordinate system is calculated from the position vector of the earth observation satellite in the geocentric inertial coordinate system and the velocity vector in the geocentric inertial coordinate system at the estimated time, and then the projection of the relative position vector of the sub-satellite point and the ground target in the orbital coordinate system at the estimated time is calculated; the expressions of the target roll angle and target pitch angle at the estimated time are obtained by combining the attitude angle of the earth observation satellite; The target pitch angle expression is iterated by a numerical method to obtain the over-the-top moment, and then the target roll angle is determined based on the over-the-top moment; The over-the-top moment corresponding to when the target roll angle satisfies the maximum roll angle constraint is used as the selected over-the-top moment in the observation time window; The observation time window corresponding to the selected overpass time is obtained by iterative calculation based on the start and end time constraints of the observation time window, and is used as the final agile satellite earth observation time window.

2. The method for calculating the time window for agile satellite earth observation according to claim 1, characterized in that: The calculation method of the six satellite orbit numbers at time t is: The six elements of the satellite orbit are expressed as [ae iΩωM], where a is the semi-major axis of the orbit, e is the eccentricity, i is the inclination, Ω is the right ascension of the ascending node, ω is the angular distance of the periapsis, and M is the mean anomaly; In the orbit recursion, the influence of the non-spherical gravity J2 perturbation term is considered, and the time t0 is taken as the initial time of the flight. The six satellite orbit elements at time t are calculated based on the linearized J2 perturbation equation: Where a0 is the initial value of the semi-major axis of the orbit at time t0, e0 is the initial value of the eccentricity at time t0, i0 is the initial value of the inclination at time t0, Ω0 is the initial value of the right ascension of the ascending node at time t0, ω0 is the initial value of the angular distance of the pericenter at time t0, and M0 is the initial value of the mean anomaly at time t0; J2 is the perturbation coefficient, n is the average orbital angular velocity, μ is the Earth's gravitational constant; is the earth's equatorial radius, p is the semi-diameter, p = a0(1-e 2 ).

3. The method for calculating the time window for agile satellite earth observation according to claim 2, characterized in that: The position vector of the Earth observation satellite in the geocentric inertial coordinate system at time t is expressed as r ECI : Where f is the true anomaly angle; The velocity vector in the geocentric inertial coordinate system is represented by v ECI :

4. The method for calculating the time window for earth observation by an agile satellite according to claim 3, characterized in that: The position vector of the Earth observation satellite in the geocentric fixed coordinate system is expressed as r ECEF : r ECEF ＝R Z (α Gt )r ECI ， Where R Z is the rotation matrix of the earth observation satellite around the Z axis in the geocentric inertial coordinate system, α Gt is Greenwich Mean Sidereal Time, α G0 is the initial Greenwich mean sidereal time, is the angular velocity of the Earth's rotation.

5. The method for calculating the time window for agile satellite earth observation according to claim 4, characterized in that: The analytical expression of the subsatellite point trajectory with respect to time is obtained as follows: According to r ECEF =[r x ,r y ,r z ] T Calculate the geocentric longitude λ c and geocentric latitude Where r x is the X-axis coordinate of the geocentric fixed coordinate system, r y is the Y-axis coordinate of the geocentric fixed coordinate system, r z is the Z-axis coordinate of the geocentric fixed coordinate system; Geographic longitude λ d for: Where u is the latitude angle: u = ω + f; According to the latitude argument u, the geocentric latitude It is expressed as: Geographic latitude for: In the formula is the first eccentricity of the Earth ellipsoid; By the geographical longitude λ at all times d and geographic latitude The sub-satellite point represented by is used to obtain the analytical expression of the sub-satellite point trajectory with respect to time.

6. The method for calculating the time window for agile satellite earth observation according to claim 5, characterized in that: The method to filter out all the moments when the latitude of the sub-satellite point is equal to that of the ground target is: When the latitude of the sub-satellite point is equal to that of the ground target, the latitude argument u satisfies: Where N is the number of satellite orbits; For a near-circular orbit: f≈M; then the latitude argument u is linearly related to t, and all moments when the sub-satellite point and the ground target latitude are equal can be calculated by the linearized J2 perturbation equation.

7. The method for calculating the time window for agile satellite earth observation according to claim 6, characterized in that: The method for determining the estimated time when there is a visible time window is: Calculate the haversine distance d: In the formula is the current geographic latitude difference between the sub-satellite point and the ground target, is the current geographic latitude of the subsatellite point, is the current geographical latitude of the ground target; Δλ is the current geographic longitude difference between the sub-satellite point and the ground target; If the haversine distance d is less than the set distance threshold, the current time is used as the estimated time.

8. The method for calculating the time window for agile satellite earth observation according to claim 7, characterized in that: The three-axis unit vector is expressed as [ijk] T , where i is the X-axis unit vector of the orbital coordinate system, j is the Y-axis unit vector of the orbital coordinate system, and k is the Z-axis unit vector of the orbital coordinate system: The relative position vector δr of the earth observation satellite pointing to the ground target in the geocentric inertial coordinate system ECI for: δr ECI =r T-ECI -r ECI , Where r T-ECI is the position vector of the ground target in the geocentric inertial coordinate system; The projection of the relative position vector between the subsatellite point and the ground target in the orbital coordinate system at the estimated time is δr VVLH : δr VVLH =[i j k] T ·δr ECI 。 9. The method for calculating the time window for agile satellite earth observation according to claim 8, characterized in that: The method for determining the time of passing the top is: The attitude angle of the Earth observation satellite includes the roll angle φ, the pitch angle θ and the yaw angle ψ. Assume ψ = 0. The attitude rotation matrix R in the orbital coordinate system is yx =R y (θ)R x (φ), R x is the rotation matrix of the earth observation satellite around the X axis in the orbital coordinate system, R y is the rotation matrix of the earth observation satellite around the Y axis in the orbital coordinate system; Assuming that the initial attitude of the Earth observation satellite payload points to the Z axis of the orbital coordinate system, then: The expressions of target roll angle and target pitch angle at the estimated time are obtained: Where δr x is the estimated time projection δr VVLH X-axis coordinate, δr y is the estimated time projection δr VVLH Y-axis coordinate, δr z is the estimated time projection δr VVLH The Z-axis coordinate of The over-the-top moment is defined as the moment when the pitch angle θ = 0. In the neighborhood of the estimated time, the expression of the pitch angle θ is iterated by a numerical method to obtain the over-the-top moment t over ; Set the top time t over Substitute the target roll angle expression into the target roll angle and calculate the target roll angle; If the target roll angle satisfies the maximum roll angle constraint, the current over-the-top time t over The selected passing moment as the existence observation time window.

10. The method for calculating the time window for agile satellite earth observation according to claim 9, characterized in that: The method for calculating the time window of agile satellite earth observation is: Let the starting time of the observation time window be t start and the end time t end Satisfy the maximum pitch angle constraint of the earth observation satellite: θ(t start )=θ max ,θ(t end )=-θ max , θ max is the maximum elevation angle of the Earth observation satellite; Set the starting time t start and the end time t end and the time t over The time interval is Δt: In t over ±Δt neighborhood, the final starting time t is determined iteratively using a numerical method for the pitch angle θ start and the final termination time t end , the final obtained [t start ,t end ] as the ultimate agile satellite earth observation time window.

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